x^2 + y^2<=a^2/4 and y>=0 and y^2>=(a/2 + x) (1/2 a (2 r - 1) - x) and 1/4 a^2 (2 r - 1) + x^2 + y^2>=a r x

shoemaker's knife

a>0 and 0

A = 1/4 π a^2 (1 - r) r

x^_ = (1/2 a (-1/2 + r), a/π)

J_x invisible comma x = -1/64 π a^4 (r - 1) r ((r - 1) r + 2)

J_y invisible comma y = -1/64 π a^4 (r - 1) r (5 (r - 1) r + 2)

J_zz = 1/32 π a^4 r (-3 r^3 + 6 r^2 - 5 r + 2)

J_x invisible comma y = 1/24 a^4 (r - 1) r (2 r - 1)

r_x = 1/4 a sqrt((r - 1) r + 2) r_y = 1/4 a sqrt(5 (r - 1) r + 2)

p = 2 π a

a

concave laminae | curvilinear laminae